I have been wondering about this too since I read 'Peaceful Death, Joyful Rebirth' and from what I have gathered they are more or less interchangeable.
Venerable Thubten Chodron stated this in a recent teaching on the Amitabha practice, I do not know which episode it was but they are certainly worth watching all of them:https://www.youtube.com/playlist?list=P ... YLfiMs8sc0

Personally I have experienced an auspicious effect with the Ami Deva variation and this is the mantra that was taught to me when I received the Amitabha empowerment from Ayang Rinpoche.
I would care to hear what your impression is of these two mantra variations and if you have experienced a difference between them in their vibration or frequency.

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Namo Amitabha Buddhaya

'If you want to find the secrets of the universe, think in terms of energy, frequency and vibration.'
— Nikola Tesla

Yup. But many of the Tibetan practices for Amitabha are tantric, so...

PS It is acceptable to just chant the seed syllable too: HRIH

"My religion is not deceiving myself."Jetsun Milarepa 1052-1135 CE

"Butchers, prostitutes, those guilty of the five most heinous crimes, outcasts, the underprivileged: all are utterly the substance of existence and nothing other than total bliss."The Supreme Source - The Kunjed Gyalpo
The Fundamental Tantra of Dzogchen Semde

Yup. But many of the Tibetan practices for Amitabha are tantric, so...

I figured that there may be Amitabha Sadhanas that don't require lung? Similar to those Shakyamuni, Medicine Buddha, Chenrezig and Tara practices that you can practice without lung.

There may well be, but I have not seen one yet. Check the FPMT website, they generally have many sutric sadhana available.

"My religion is not deceiving myself."Jetsun Milarepa 1052-1135 CE

"Butchers, prostitutes, those guilty of the five most heinous crimes, outcasts, the underprivileged: all are utterly the substance of existence and nothing other than total bliss."The Supreme Source - The Kunjed Gyalpo
The Fundamental Tantra of Dzogchen Semde

True, within the ancient culture of India the terms deity, divinity and god being are rather synonymous for the same phenomenon if I am not mistaken.

As Grigoris stated the Amitabha mantra can be practised without receiving an initiation.
With regard to your question about whether a Amitabha Sadhana practise exists that can be practised without receiving an empowerment is something I too am uncertain about as I also have not encountered one.

Lotsawa House does not mention the necessity to have received the appropriate tantric empowerment in order to practice this sādhana.
If you want to be sure whether this is the case, I suggest you contact them.

I hope this is the sādhana that may fulfil your wish.

__/\__

'If you want to find the secrets of the universe, think in terms of energy, frequency and vibration.'
— Nikola Tesla

"Butchers, prostitutes, those guilty of the five most heinous crimes, outcasts, the underprivileged: all are utterly the substance of existence and nothing other than total bliss."The Supreme Source - The Kunjed Gyalpo
The Fundamental Tantra of Dzogchen Semde

I agree! It is a phenomenal prayer, especially when practised regularly or as Karma Chagme advises:

"If possible, recite this aspiration every day, if not, once every month or every year. When you are at leisure, face the
west and recollect the realm of Sukhavati and Buddha Amitabha. With palms joined in devotion and recite this aspiration prayer with one-pointed faith, it is said that your obstacles in this life will be dispelled. There is no doubt you will be reborn in Sukhavati after this life."

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'If you want to find the secrets of the universe, think in terms of energy, frequency and vibration.'
— Nikola Tesla

Lotsawa House does not mention the necessity to have received the appropriate tantric empowerment in order to practice this sādhana.
If you want to be sure whether this is the case, I suggest you contact them.

I hope this is the sādhana that may fulfil your wish.

__/\__

I havn't messaged Lotsawa House yet and from the looks of that text it looks like it would need a rLung but I recently found this simple and concise sādhana compiled by Lama Thubten Yeshe. I emailed Sravasti Abbey and was told it does not require a transmission to practice. https://thubtenchodron.org/2017/07/amitabha-sadhana/

The different sūtras in accord with the emptiness
taught by the Sugata are definitive in meaning;
One can understand that all of those Dharmas in
which a sentient being, individual, or person are taught are provisional in meaning.

Lotsawa House does not mention the necessity to have received the appropriate tantric empowerment in order to practice this sādhana.
If you want to be sure whether this is the case, I suggest you contact them.

I hope this is the sādhana that may fulfil your wish.

__/\__

I havn't messaged Lotsawa House yet and from the looks of that text it looks like it would need a rLung but I recently found this simple and concise sādhana compiled by Lama Thubten Yeshe. I emailed Sravasti Abbey and was told it does not require a transmission to practice. https://thubtenchodron.org/2017/07/amitabha-sadhana/

Magnificent! Glad to see you have found this beautiful, and accessible practise.
Have you watched Sravasti Abbey's venerable Thubten Chodron's teachings on the Amitabha practice?
It is a quite comprehensive series of teachings that is conducive to the sādhana:https://www.youtube.com/playlist?list=P ... YLfiMs8sc0

__/\__

'If you want to find the secrets of the universe, think in terms of energy, frequency and vibration.'
— Nikola Tesla